Topology 2nd Edition

I've gone through most of this book and did many of the problems. The sections I skipped are the section on nets, the "review section" in chapter 4, the existence of a continuous nowhere-differentiable function, Dimension Theory, and all of Chapter 10 (Separation Theorems in the Plane), the Classification Theorem, and Constructing Compact Surfaces.This is definitely my favorite math book. The two other books I've read this semester (Conway's Complex Analysis, and Rudin's Real and Complex Analysis) simply don't compare. In fact I'm afraid I'll always find fault with every other math book, after reading this one. There's alot of good expository prose, many examples and diagrams, and if you pay attention to details, and struggle to supply missing ones, you won't miss a beat and will succeed (unlike sometimes in Rudin's text). The problems are appropriate; very few are mindless, most do require a little thought, but a motivated student could solve most or all of them in a reasonable amount of time. There are no sudden breaks in proofs or in the text that are relegated as exercises (unless it's a repeat of a previous proof), and although results from previous exercises are sometimes used, he always states the necessary hypotheses. The book is self-contained - he begins with 70+ pages of naive set theory, for instance (not a prerequisite for the rest of the book).I feel that reading this book and working its problems has given me a solid and comprehensive grounding in basic topology, and this book does go beyond what's usually taught in a first topology course, and the second half of the book is all algebraic topology. Here I found the review of abelian groups, free products and free groups to be extremely helpful, though I did still have to contemplate these alot on my own afterwards. The Seifert-Van Kampen theorem was also well-presented; he presents it as a pushout diagram. In the last chapter, as a nice application, he proves using linear graphs that subgroups of free groups are free.I just simply love this book, but to be fair, I do have some minor qualms.(1) There are a few obvious typos, and I didn't find more than six(2) I believe one step in the proof of Lemma 68.9 is incorrect; this arises from a definitional issue of the subgroup generated by a subset. earlier, he assumed the subset was itself a subgroup, but now he's assuming it's arbitrary. the correct definition is on the next page, and the method of proof, with this definition, does give the right result; almost nothing changes in the proof(3) In Theorem 68.4, the monomorphism and generating assumptions aren't necessary(4) Problem #2 on page 438: I think the X_i should be path-connected, and Wikipedia is in agreement with this. I tried passing to path-components, which solved one problem but gave me others. On the other hand, if you assume path-connectedness, the proof is is the right level of difficulty.(5) He gives an exercise regarding absolute retracts and adjunction spaces. I think he should've elaborated more on adjunction spaces, as it does involve new notions (e.g. free/topological union). Also his definition of adjunction space is incomplete, as compared to other definitions I found(6) The book binding is horrible (it's the same with his other book, "Analysis on Manifolds"). If you're paying 100+ dollars for a book, you should expect to receive something very pretty, but the typesetting of this book is quite dull, and the book falls apart easily (mine is in many pieces).In conclusion I highly recommend this book for self-study, and for seeing how math books can and should be written. I hope Munkres writes more textbooks, I'd read every single one of them.

I used to own the first (1975) edition of this title since the late 1990s, but eventually purchased the new edition as well, and donated the old book to our campus library. Despite having very close similarity to the text by Stephen Willard (1970, Dover issue 2004) which points to the fact that both authors must have used the same source articles, Munkres's book stands out as one of the best rigorous introductions for a beginning graduate student. It covers all the standard material for a first course in general topology starting with a full chapter on set theory, and now in the second edition includes a rather extensive treatment of elementary algebraic topology. The style of writing is student-friendly, the topics are nicely motivated, (counter-)examples are given where they were needed, many diagrams provided, the chapter exercises relevant with the correct degree of difficulty, and there are virtually no typos. The 2nd edition fine-tunes the exposition throughout, including a better paragraph formatting of the material and also greatly expands on the treatment of algebraic topology, making up for 14 total chapters as opposed to eight in the first edition. I particularly found useful the discussion of the separation axioms and metrization theorems in the first part, and the classification of surfaces and covering spaces in the second part.In my opinion, after going through the discussion of algebraic topology in Munkres, the students should be ready to move forward to a (now standard) text such as Hatcher, for further coverage of homotopy, homology and cohomology theories of spaces. Eventhough a few contending general topology texts - such as a recent title published in the Walter Rudin Series - have started to hit the academic markets, Munkres will no doubt remain as the classic, tried-and-trusted source of learning and reference for generations of mathematics students. This is despite the fairly high price tag which could stop some students from buying their own copies, hence encouraging instructors to choose some of the cheaper topology paperbacks readily available through the Dover publications. Also the majority of Munkres's readers would have wished to see more hints and answers provided at the back so as to make the text more helpful for self-study. (I remember suffering from and being lost with my Munkres topology homework exercises in 1998-1999, during my first year of graduate school.) It later became evident to me that those who are newcomers to the topic or are merely testing the waters, should try Fred H. Croom's 1989 topology text, since the latter is a more accessible title similar in the exposition and selection of topics on Munkres (and Willard for that matter), thus nicely serving as a prerequisite for either of the more advanced books.A couple of ending remarks: A reviewer has correctly mentioned here that Dr. Munkres does not include differential topology in his presentation. This is because of the length consideration, given that he has already written a separate monograph on the topic. In fact it's also necessary to first get a handle on a fair amount of algebraic topology such as the notions of homotopy, fundamental groups, and covering spaces for a full-fledged treatment of the differential aspect. In any case, one high-level reference for a rigorous excursion into this area is the Springer-Verlag GTM title by Morris W. Hirsch which includes introductions to the Morse and cobordism theories. I'd also like to mention that another decent book on general topology, unfortunately out of print for quite some time, is a treatise by "James Dugundji" (Prentice Hall, 1965). The latter would complement Munkres, as for instance Dugundji discusses ultrafilters and some of the more analytical directions of the subject. It's a pity that Dover in particular, has not yet published this gem in the form of one of their paperbacks.

The first part of the book (point-set topology) is excellent. I felt this way a decade ago as a student and still feel this way having used it recently as an instructor. On the other hand, the second part (fundamental group) seems weaker to me. I would have presented (and did in class) a number of things differently. There are far fewer exercises in the second part and they tend to be far less interesting than in the first part. However, Chapter 12, classification of surfaces, is a real gem in my view; I am not aware of another source where this classical topic is done so clearly. For example, try to find a place where the cohomology ring of surfaces (including unorientable ones) is worked out, but this can be obtained immediately from from the Classification Theorem in Chapter 12.

The best topology book, suitable for both undergraduate and graduate students. Contains all the necessary topics for a «working mathematician». The one "bad" thing I’ll say is that the format is weird to say the least. The book could’ve been twice smaller if not for comically large spacings from the text to the edges. But other than that, the quality is great!

La stampa e la qualità della carta sono all'altezza delle aspettative cosa rara nelle edizioni italiane. Il contenuto mi sembra buono ma sarà questione di tempo e di serio approfondimento. Ottimo venditore e ottimo acquisto.

Best book to understand spaces or all other topology cincepts. Generalised manner to explain things.Rhe good thing is it eoes not matter for how long you are out of touch with set theory, you need not to look for other books to start from scratch, you will get everything in this book even in a much better detailed manner.

The book arrived on time in good condition, minimal damages sustained. The book itself is good, worth the price.

Eines der besten Topologie Bücher. Klar und verständlich geschrieben. Ein sehr gutes Buch für einen ersten Topologie Kurs. Auch danach immer noch sehr hilfreich.